The luminosity function (hereafter LF) is one of the most powerful tools to study the galaxy population of a group/cluster of galaxies. It is given by the number density of galaxies per luminosity interval and it is usually described parametrically with the Schechter function [1]}. The main parameters are the characteristic magnitude (M\(^*\) ) and the faint-end slope (\(\alpha \) ). The former describes the bright part of the LF, whereas the latter is related to the dwarf galaxy population. A debate is ongoing on the universality of the LF: in fact, photometric studies found that LFs in clusters are steeper than in the field [2]}, [3]}. On the other hand, spectroscopic studies found no differences in the \(\alpha \)  parameters of the field and clusters, finding a general value of \(\alpha \sim -1.3\)  [4]}
